runzun wrote:In a room filled with 7 people, 4 people have exactly 1 sibling in the room and 3 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
5/21
3/7
4/7
5/7
16/21
oa after some discussion
Probability of NOT selecting siblings = 1- probability of selecting siblings
Let us take the 7 people as A, B, C, D, E, F, G.
Out of these 7 people, 4 have exactly 1 sibling, which can be A-B (Group 1), C-D (Group 2); and people with exaclty two siblings can be E-F-G (Group 3).
Out of 7 people any two people can be selected in 7C2 ways = 21
Probability that two persons selected are from 1st group = 2C2 = 1
probability that two persons selected are from 2nd group = 2C2 = 1
probability that two persons selected are from 3rd group = 3C2 = 3
Therefore, probability that selected people will be siblings = (1 + 1+ 3)/21 = 5/21
Probability of NOT selecting siblings = 1 - 5/21 = 16/21
The correct answer is
E.
